A high-precision study of the hopfield model in the phase of broken replica symmetry

Kohring, G.A.

doi:10.1007/bf01025863

Cited by 33 publications

(27 citation statements)

References 11 publications

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“…In both cases, simulation data are available for comparison with theoretical results [7][8][9]. The RS approximations reproduce previously known results as they should.…”

Section: Resultssupporting

confidence: 61%

“…We have obtained 1RSB and 2RSB corrections to RS results, which are much smaller than expected from simulation results [7][8][9] or previously reported for the standard model atā = 1/2 [3]. In all cases the 1RSB and 2RSB storage capacities obtained were found to be smaller than those attainable in the RS approximation at finite temperature.…”

Section: Summary and Discussionmentioning

confidence: 45%

“…In the previous section, we have seen that 1RSB or 2RSB approximations to the mean-field solution of generalized Hopfield-type models yield a slight increase of the storage capacities of these models, but this increase was found to be much smaller than probably expected from simulation results [7][8][9], or previously reported [3]. In all cases , the resulting storage capacity was found to be smaller than that maximally attainable in the RS approximation at finite temperature.…”

Section: Relation With Rsb In the Sk-modelmentioning

confidence: 63%

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The Replica Symmetry Breaking

Dotsenko¹

1995

World Scientific Lecture Notes in Physics

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“…In both cases, simulation data are available for comparison with theoretical results [7][8][9]. The RS approximations reproduce previously known results as they should.…”

Section: Resultssupporting

confidence: 61%

Section: Summary and Discussionmentioning

confidence: 45%

Section: Relation With Rsb In the Sk-modelmentioning

confidence: 63%

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The Replica Symmetry Breaking

Dotsenko¹

1995

World Scientific Lecture Notes in Physics

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“…the replica symmetry of q being inherited by r due to (14). This ansatz allows for an easy evaluation of all terms appearing in (8), (13) and (14), as well as for an analytic continuation of the results to n → 0. As the n → 0 limit is taken one gets…”

Section: The Replica Symmetric Approximationmentioning

confidence: 99%

Replica symmetry breaking in attractor neural network models

Steffan

Kühn

1994

Z. Physik B - Condensed Matter

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The phenomenon of replica symmetry breaking is investigated for the retrieval phases of Hopfield-type network models. The basic calculation is done for the generalized version of the standard model introduced by Horner [1] and by Perez-Vicente and Amit [2] which can exhibit low mean levels of neural activity. For a mean activity ¯ a = 1/2 the Hopfield model is recovered. In this case, surprisingly enough, we cannot confirm the well known one step replica symmetry breaking (1RSB) result for the storage capacity which was presented by Crisanti, Amit and Gutfreund [3] (α 1RSB c ≃ 0.144). Rather, we find that 1RSB-and 2RSB-Ansätze yield only slightly increased capacities as compared to the replica symmetric value (α 1RSB c ≃ 0.138 186 and α 2RSB c ≃ 0.138 187 compared to α RS c ≃ 0.137 905), significantly smaller also than the value α sim c = 0.145 ± 0.009 reported from simulation studies. These values still lie within the recently discovered reentrant phase [4]. We conjecture that in the infinite Parisi-scheme the reentrant behaviour disappears as is the case in the SK-spin-glass model (Parisi-Toulouse-hypothesis). The same qualitative results are obtained in the low activity range.

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“…testing experiments of such a kind one is satisfied by registration of steady tendency of conversion of the graph ( ) m α into the step function [8], [9].…”

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confidence: 99%

Investigation of generalized Hopfield model by statistical physics methods

Kryzhanovsky

Litinskii

2010

The 2010 International Joint Conference on Neural Networks (IJCNN)

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The proposed generalization of the Hopfield model consists in assigning different weight coefficients to input patterns that are used to construct the Hebb connection matrix. Application of statistical physics methods to such a system gives unexpected results even for the simplest variant of differences of weight coefficients. Namely, there are unusual behaviors of the critical value of the load parameter and of the overlap of the state with the pattern.

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A high-precision study of the hopfield model in the phase of broken replica symmetry

Cited by 33 publications

References 11 publications

The Replica Symmetry Breaking

The Replica Symmetry Breaking

Replica symmetry breaking in attractor neural network models

Investigation of generalized Hopfield model by statistical physics methods

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